Question: Divide the following complex numbers: $\dfrac{8 e^{5\pi i / 4}}{2 e^{2\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8 e^{5\pi i / 4}$ ) has angle $\frac{5}{4}\pi$ and radius 8. The second number ( $2 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius 2. The radius of the result will be $\frac{8}{2}$ , which is 4. The angle of the result is $\frac{5}{4}\pi - \frac{2}{3}\pi = \frac{7}{12}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{7}{12}\pi$.